Changinng in-game Armature Object's Armature Data
If you are talking about Armature datablock, it is similar as changing the mesh data for mesh object:

  

If you are talking about changing Action Data for armature, there are two places to go, depends on your actual need:



For BGE action, you may take the 2nd one.

PS: Action Data exchanging between armatures requires high similarity, in other words, same hierachy, same bone count, same bone names, etc. Otherwise it will not work as expected.